Why Didn't the East Fall?

The west had an incredibly long rhine frontier and an incredibly long danube frontier to contend with. Once any portion of those frontiers was reached, our barbarian horde could pretty much go wherever it wanted. After the invasion of four o five, this is exactly what happened in the east. Any attempt to cross the hellespont and they' run smack into constantinople and its impenetrable walls. The military shocks that hit the west in the four hundreds rapidly depleted its economic output. And as barbarian nations set up autonomous zones and wealthy nobles withdrew to their estates, the central government was cut off more and more for bat little wealth was available. This ly did not happen